Đưa các phân thức sau về cùng mẫu
a) \(\dfrac{x}{2x^2+7x-15}\); \(\dfrac{x+2}{x^2+3x-10}\); \(\dfrac{1}{x+5}\)
b) \(\dfrac{1}{-x^2+3x-2}\); \(\dfrac{1}{x^2+5x-6}\); \(\dfrac{1}{-x^2+4x-3}\)
c)\(\dfrac{3}{x^3-1}\); \(\dfrac{2x}{x^2+x+1}\); \(\dfrac{x}{x-1}\)
d)\(\dfrac{x}{x^2-2xy+y^2-x^2}\); \(\dfrac{y}{x^2+2yz-y^2-z^2}\); \(\dfrac{z}{x^2-2xz-y^2+z^2}\)
a: \(\dfrac{x}{2x^2+7x-15}=\dfrac{x}{\left(x+5\right)\left(2x-3\right)}=\dfrac{x^2-2x}{\left(x+5\right)\left(x-2\right)\left(2x-3\right)}\)
\(\dfrac{x+2}{x^2+3x-10}=\dfrac{x+2}{\left(x+5\right)\left(x-2\right)}=\dfrac{\left(x+2\right)\left(2x-3\right)}{\left(2x-3\right)\left(x+5\right)\left(x-2\right)}\)
\(\dfrac{1}{x+5}=\dfrac{\left(2x-3\right)\left(x-2\right)}{\left(2x-3\right)\left(x-2\right)\left(x+5\right)}\)
b: \(\dfrac{1}{-x^2+3x-2}=\dfrac{-1}{\left(x-1\right)\left(x-2\right)}=\dfrac{-\left(x+6\right)\left(x-3\right)}{\left(x-1\right)\left(x-2\right)\left(x+6\right)\left(x-3\right)}\)
\(\dfrac{1}{x^2+5x-6}=\dfrac{1}{\left(x+6\right)\left(x-1\right)}=\dfrac{\left(x-2\right)\left(x-3\right)}{\left(x+6\right)\left(x-1\right)\left(x-2\right)\left(x-3\right)}\)
\(\dfrac{1}{-x^2+4x-3}=\dfrac{-1}{\left(x-1\right)\left(x-3\right)}=\dfrac{-\left(x-2\right)\left(x+6\right)}{\left(x-1\right)\left(x-3\right)\left(x+6\right)\left(x-2\right)}\)
c: \(\dfrac{3}{x^3-1}=\dfrac{3}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\dfrac{2x}{x^2+x+1}=\dfrac{2x\left(x-1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
\(\dfrac{x}{x-1}=\dfrac{x\left(x^2+x+1\right)}{\left(x-1\right)\left(x^2+x+1\right)}\)
Làm tính cộng các phân thức :
a) \(\dfrac{11x+13}{3x-3}+\dfrac{15x+17}{4-4x}\)
b) \(\dfrac{2x+1}{2x^2-x}+\dfrac{32x^2}{1-4x^2}+\dfrac{1-2x}{2x^2+x}\)
c) \(\dfrac{1}{x^2+x+1}+\dfrac{1}{x^2-x}+\dfrac{2x}{1-x^3}\)
d) \(\dfrac{x^4}{1-x}+x^3+x^2+x+1\)
Giải các phương trình sau:
\(a.\dfrac{4x-5}{x-1}=2+\dfrac{x}{x-1}\)
\(b.\dfrac{7}{x+2}=\dfrac{3}{x-5}\)
\(c.\dfrac{14}{3x-12}-\dfrac{2+x}{x-4}=\dfrac{3}{8-2x}-\dfrac{5}{6}\)
\(d.\dfrac{x+1}{x-1}-\dfrac{x-1}{x+1}=\dfrac{16}{x^2-1}\)
TK
https://lazi.vn/edu/exercise/giai-phuong-trinh-4x-5-x-1-2-x-x-1-7-x-2-3-x-5
a: \(\Leftrightarrow4x-5=2x-2+x\)
=>4x-5=3x-2
=>x=3(nhận)
b: =>7x-35=3x+6
=>4x=41
hay x=41/4(nhận)
c: \(\Leftrightarrow\dfrac{14}{3\left(x-4\right)}-\dfrac{x+2}{x-4}=\dfrac{-3}{2\left(x-4\right)}-\dfrac{5}{6}\)
\(\Leftrightarrow\dfrac{28}{6\left(x-4\right)}-\dfrac{6\left(x+2\right)}{6\left(x-4\right)}=\dfrac{-9}{6\left(x-4\right)}-\dfrac{5\left(x-4\right)}{6\left(x-4\right)}\)
\(\Leftrightarrow28-6x-12=-9-5x+20\)
=>-6x+16=-5x+11
=>-x=-5
hay x=5(nhận)
d: \(\Leftrightarrow x^2+2x+1-\left(x^2-2x+1\right)=16\)
\(\Leftrightarrow4x=16\)
hay x=4(nhận)
Giải phương trình:
a) \(\dfrac{x^2-x-6}{x-3}=0\)
b) \(\dfrac{x+5}{3x-6}-\dfrac{1}{2}=\dfrac{2x-3}{2x-4}\)
c) \(\dfrac{12}{1-9x^2}=\dfrac{1-3x}{1+3x}-\dfrac{1+3x}{1-3x}\)
d) \(\dfrac{x+5}{x-1}=\dfrac{x+1}{x-3}-\dfrac{8}{x^2-4x+3}\)
e) \(\dfrac{x+1}{x-2}-\dfrac{5}{x+2}=\dfrac{12}{x^2-4}+1\)Thể loại truyện
a) ĐKXĐ: \(x\ne3\)
Ta có: \(\dfrac{x^2-x-6}{x-3}=0\)
\(\Leftrightarrow\dfrac{\left(x+2\right)\left(x-3\right)}{x-3}=0\)
Suy ra: x+2=0
hay x=-2(thỏa ĐK)
Vậy: S={-2}
d)
ĐKXĐ: \(x\notin\left\{1;3\right\}\)
Ta có: \(\dfrac{x+5}{x-1}=\dfrac{x+1}{x-3}-\dfrac{8}{x^2-4x+3}\)
\(\Leftrightarrow\dfrac{\left(x+5\right)\left(x-3\right)}{\left(x-1\right)\left(x-3\right)}=\dfrac{\left(x+1\right)\left(x-1\right)}{\left(x-3\right)\left(x-1\right)}-\dfrac{8}{\left(x-1\right)\left(x-3\right)}\)
Suy ra: \(x^2-3x+5x-15=x^2-1-8\)
\(\Leftrightarrow2x-15+9=0\)
\(\Leftrightarrow2x-6=0\)
hay x=3(loại)
Vậy: \(S=\varnothing\)
Rút gọn
a)\(\dfrac{x}{x+1}+\dfrac{1}{x-1}-\dfrac{2x}{1-x^2}\)
b)\(\dfrac{x}{x-2}-\dfrac{4x}{x^2-4}-\dfrac{2}{x+2}\)
c)\(\dfrac{2x^2-3x-9}{x^2-9}-\dfrac{x}{x+3}-\dfrac{x+3}{3-x}\)
d)\(\dfrac{x+3}{x-2}+\dfrac{x+2}{1-x}-\dfrac{4x-x^2}{x^2-3x+2}\)
giúp mik vs
cảm ơn <3
a: \(=\dfrac{x^2-x+x+1+2x}{\left(x-1\right)\left(x+1\right)}=\dfrac{\left(x+1\right)^2}{\left(x-1\right)\left(x+1\right)}=\dfrac{x+1}{x-1}\)
b: \(=\dfrac{x^2+2x-4x-2x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2-4x+4}{\left(x-2\right)\left(x+2\right)}=\dfrac{x-2}{x+2}\)
c: \(=\dfrac{2x^2-3x-9-x^2+3x+x^2+6x+9}{\left(x-3\right)\left(x+3\right)}\)
\(=\dfrac{2x^2+6x}{\left(x-3\right)\left(x+3\right)}=\dfrac{2x}{x-3}\)
Bài 1:tính
a)\(\dfrac{x^2-2^{ }}{x\left(x-1\right)^2}+\dfrac{2-x}{x\left(1-x\right)^2}\)
b)\(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}\)
c)\(\dfrac{x}{x-1}+\dfrac{2}{x^2+x+1}+\dfrac{4x^2-1}{1-x^3}\)
\(a,=\dfrac{x^2-2+2-x}{x\left(x-1\right)^2}=\dfrac{x\left(x-1\right)}{x\left(x-1\right)^2}=\dfrac{1}{x-1}\\ b,=\dfrac{6x-3+6x^2-6x+2x^2+1}{2x\left(2x-1\right)}=\dfrac{8x^2-2}{2x\left(2x-1\right)}\\ =\dfrac{2\left(2x-1\right)\left(2x+1\right)}{2x\left(2x-1\right)}=\dfrac{2x+1}{x}\\ c,=\dfrac{x^3+x^2+x+2x-2+4x^2-1}{\left(x-1\right)\left(x^2+x+1\right)}=\dfrac{x^3+5x^2+3x-3}{x^3-1}\)
a) \(\dfrac{x+3}{x-3}-\dfrac{x-3}{x+3}=\dfrac{36}{x^2-9}\)
b) \(\dfrac{2x-1}{x+4}-\dfrac{1-3x}{x-4}=5+\dfrac{96}{x^2-16}\)
c) \(\dfrac{x+3}{x+1}-\dfrac{x-1}{x}=\dfrac{3x^2+4x+1}{x\left(x+1\right)}\)
Cộng các phân thức khác mẫu thức :
a) \(\dfrac{5}{6x^2y}+\dfrac{7}{12xy^2}+\dfrac{11}{18xy}\)
b) \(\dfrac{4x+2}{15x^3y}+\dfrac{5y-3}{9x^2y}+\dfrac{x+1}{5xy^3}\)
c) \(\dfrac{3}{2x}+\dfrac{3x-3}{2x-1}+\dfrac{2x^2+1}{4x^2-2x}\)
d) \(\dfrac{x^3+2x}{x^3+1}+\dfrac{2x}{x^2-x+1}+\dfrac{1}{x+1}\)
Làm tính cộng các phân thức sau :
a) \(\dfrac{5}{2x^2y}+\dfrac{3}{5xy^2}+\dfrac{x}{y^3}\)
b) \(\dfrac{x+1}{2x+6}+\dfrac{2x+3}{x\left(x+3\right)}\)
c) \(\dfrac{3x+5}{x^2-5x}+\dfrac{25-x}{25-5x}\)
d) \(x^2+\dfrac{x^4+1}{1-x^2}+1\)
e) \(\dfrac{4x^2-3x+17}{x^3-1}+\dfrac{2x-1}{x^2+x+1}+\dfrac{6}{1-x}\)
